Collinearity and Distance (3.3.1)

Question 1

• Points that fall on the same line are collinear points.

Answer 1

• Points that fall on the same line are collinear points.

Question 2

• Three points are collinear if, for some pair of lengths between two points, their sum is equal to the remaining third length
between two points.

Answer 2

• Three points are collinear if, for some pair of lengths between two points, their sum is equal to the remaining third length
between two points.

Question 3

• Three points are not collinear if, for every pair of lengths between two points, their sum is greater than the remaining third
length between two points. This result indicates that the points form a triangle.

Answer 3

• Three points are not collinear if, for every pair of lengths between two points, their sum is greater than the remaining third
length between two points. This result indicates that the points form a triangle.

Question 4

• Pythagorean Theorem: a^2+b^2=c^2.

Answer 4

• Pythagorean Theorem: a^2+b^2=c^2.

Question 5

• If you are given three points and you square the three lengths between pairs of points, you can tell that the points form a
right triangle if the sum of any two of the squared lengths equals the third squared length.

Answer 5

• If you are given three points and you square the three lengths between pairs of points, you can tell that the points form a
right triangle if the sum of any two of the squared lengths equals the third squared length.

Question 6

• The distance between any two points is found by squaring the difference in their x-values and adding it to the squared
difference in their y-values, then finding the square root of the sum.

Answer 6

• The distance between any two points is found by squaring the difference in their x-values and adding it to the squared
difference in their y-values, then finding the square root of the sum.

Question 7

Figuring out whether these points are collinear becomes a
matter of calculating the three lengths and checking to see if
any two of them add up to the third one.
So, let’s calculate the distance between points A and B. Set
up the formula and solve for the value.
Next, let’s find the distance between a second pair of points,
A and C. Finally, find the distance between the third pair of
points, B and C.
When you compare the three lengths, you see that two of
them added together equal the third.
Your conclusion is that the points are collinear. Your
conclusion is supported by the graph showing the location
of the three points.

Answer 7

Figuring out whether these points are collinear becomes a
matter of calculating the three lengths and checking to see if
any two of them add up to the third one.
So, let’s calculate the distance between points A and B. Set
up the formula and solve for the value.
Next, let’s find the distance between a second pair of points,
A and C. Finally, find the distance between the third pair of
points, B and C.
When you compare the three lengths, you see that two of
them added together equal the third.
Your conclusion is that the points are collinear. Your
conclusion is supported by the graph showing the location
of the three points.